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On calculating analytic centers

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On calculating analytic centers


Published August 1989
Topics COMPUTATIONS.
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Title from cover

"NPS-53-89-015."

"August 1989."

AD A215 635

Includes bibliographical references (p. 7)

The analytic center of a polytope can be calculated in polynomial time by Newton's method. This note was motivated by papers of Renegar and Shub(88) and by Ye(89). We apply Smale's(86) estimates at one point for Newton's method to the problem of finding the analytic center of a polytope. The method converges globally in the appropriate norm. The ideas are then applied to obtain a possible benchmark for path following methods. When Smale's method is tractable its power stems not only from the fact that the information is concentrated at one point. There are 2 norms to estimate, not 3 as in the Kantorovich estimate. Moreover no estimate of the inverse of the derivative operator by itself is needed. The need for the norm of the inverse by itself often makes for coarse estimates. (kr)

aq/aq cc:9116 06/25/98


Publisher Monterey, California : Naval Postgraduate School
Pages 16
Language en_US
Call number a199449
Digitizing sponsor Naval Postgraduate School, Dudley Knox Library
Book contributor Naval Postgraduate School, Dudley Knox Library
Collection navalpostgraduateschoollibrary; fedlink; americana
Notes some content may be lost due to the binding of the book.

Full catalog record MARCXML

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